The OP's DD shares three traits with my DD9 at that same age: giftedness, extroversion, perfectionism, and explosive behaviors. And they were all very closely related. The first two traits were placed in direct opposition with each other during her school day... she desperately wanted to learn something new, and she desperately wanted to have peer friends in school. She had a teacher who was forcing her to choose between the two. She could either sit by herself at the computer and learn something while the rest of the kids did a group activity, or she could join with the group and learn nothing.
Either way, she was going to have her needs go unmet. And she was never going to let her frustration show, because of her perfectionism... the idea of getting her clip moved down was horrifying to her, and she felt it important to be the best-behaved child in class.
It was this bottling up of her frustrations all day that exhausted our DD mentally, and caused her to boil over the moment she got home.
So, my advice to you would be, don't assume the reason your DD is exhausted is because of the writing.
Also, one of the ways she needed us to deal with this was to give her some serious downtime at home. We scaled way back on her organized activities and just let her play. Your DD's lying about the number of times she's practiced a piano piece may be a way of trying to tell you she needs to scale back, too.
